[SS08] Emerging Mathematical and Modeling Approaches in Community and Ecosystem Ecology

[SS08-03] Majorization theory of incidence-based beta-diversity.

*Iritani Ryosuke¹ (1. RIKEN (Japan))

Keywords:

Biodiversity,Stochasticity,Heterogeneity,Beta diversity

Beta-diversity, the spatial variations in species diversity, is central to ecology and evolution. Understanding and predicting how beta-diversity varies with environmental and biotic perturbations poses a major challenge in our modern society, especially under unprecedented global changes. However, theoretical models on the variability in beta-diversity produce mixed results. Here, we aim to predict the patterns, if any, of beta-diversity under environmental heterogeneity, using stochastic theory and majorization theory. Specifically, we use the method of Schur-convexity to investigate how beta-diversity changes with species differences and spatial heterogeneity. We find that when two sites have an equal probability of fostering each species, an equalized probability of species presence maximizes beta-diversity. This prediction is consistent with incidence-based matrix analyses of beta-diversity based on checkerboard patterns and nestedness patterns, and our analyses predict that additional patterns, e.g., “dominance”, must be considered, to make predictions of beta-diversity patterns. We also use a randomization method to predict the probability distribution of beta-diversity and mechanisms thereof, clarifying the patterns of variations in beta-diversity. Overall, our work help us better understand and predict the beta-diversity patterns in natural populations.